Question

A square metal plate of edge length 6.4 cm and negligible thickness has a total charge of 6.6 x 10-6 C. Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.71 mm from the center) by assuming that the charge is spread uniformly over the two faces of the plate. Express your answer in terms of N/C.

Answer 1

`E=9.1* 10^7 N/C`

Step-by-step explanation:

We are given that

Length of side,l=6.4 cm=
`6.4* 10^(-2) m`

1 m=100 cm

Total charge,q=
`6.6* 10^(-6) C`

We have to find the magnitude E of the electric field just off the center of the plate.

Area charge density,
`\sigma=(q)/(A)=(q)/(l^2)=(6.6* 10^(-6))/((6.4* 10^(-2))^2)`

`\sigma=16.1* 10^(-4)C/m^2`

Electric field,
`E=(\sigma)/(2\epsilon_0)`

Where
`\epsilon_0=8.85* 10^(-12)`

Substitute the values

`E=(16.1* 10^(-4))/(2* 8.85* 10^(-12))`

`E=9.1* 10^7 N/C`